Critical properties of a trapped interacting Bose gas

TL;DR

This paper introduces a theoretical approach using the projected Gross-Pitaevskii equation to analyze the critical behavior of trapped Bose-Einstein condensates, including correlation length, fluctuations, and finite-size effects.

Contribution

It develops a practical formalism for studying critical properties of trapped Bose gases, extending existing methods to include finite-size effects and experimental measurement techniques.

Findings

Calculated the critical exponent for the correlation length.

Identified clear finite-size effects in trapped systems.

Proposed an experimental method for measuring number fluctuations.

Abstract

We develop a practical theoretical formalism for studying the critical properties of a trapped Bose-Einstein condensate using the projected Gross-Pitaevskii equation. We show that this approach allows us investigate the behavior of the correlation length, condensate mode and its number fluctuations about the critical point. Motivated by recent experiments [Science {\bf 315}, 1556 (2007)] we calculate the critical exponent for the correlation length, observe clear finite-size effects, and develop characteristic length scales to characterize the finite-size influences. We extend the Binder cumulant to the trapped system and discuss an experimental method for measuring number fluctuations.